Problem: Simplify the following expression: $y = \dfrac{6x^2 - 66x + 108}{x - 9} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ y =\dfrac{6(x^2 - 11x + 18)}{x - 9} $ Then we factor the remaining polynomial: $x^2 {-11}x + {18} $ ${-9} {-2} = {-11}$ ${-9} \times {-2} = {18}$ $ (x {-9}) (x {-2}) $ This gives us a factored expression: $\dfrac{6(x {-9}) (x {-2})}{x - 9}$ We can divide the numerator and denominator by $(x + 9)$ on condition that $x \neq 9$ Therefore $y = 6(x - 2); x \neq 9$